A cone has height 8.4 cm (half of 16.8 cm) and base diameter 4.2 cm. It is melted and recast into a sphere. Find the surface area of the sphere (use π = 22/7).

Introduction / Context:We convert a cone into a sphere by melting, so volumes remain equal. From the equal volume we get the sphere radius, then compute the sphere’s surface area.

Given Data / Assumptions:

• Cone height h = 8.4 cm.
• Cone base diameter = 4.2 cm ⇒ radius r = 2.1 cm.
• π = 22/7.
• No loss of material: V_cone = V_sphere.

Concept / Approach:

• V_cone = (1/3)*π*r^2*h.
• V_sphere = (4/3)*π*R^3 ⇒ R from volume equality.
• Surface area S = 4*π*R^2.

Step-by-Step Solution:

Verification / Alternative check:Using more precise intermediate rounding still yields ≈ 55.4 cm^2, matching 55.44 sq cm among options.

Why Other Options Are Wrong:

• 60/65.58/59 sq cm: Deviate from the precise conversion steps.
• None of these: Not applicable since 55.44 sq cm fits.

Common Pitfalls:

• Using diameter instead of radius.
• Rounding too early when finding R then squaring.

Final Answer:55.44 sq cm